In this paper, we consider a similarity control problem for plants and specifications, modeled as nondeterministic automata. This problem requires us to synthesize a nondeterministic supervisor such that the supervised plant is simulated by a given specification. We assume that a supervisor can observe not only the event occurrence but also the current state of the plant. First, we derive a necessary and sufficient condition for the existence of a complete supervisor, which is a solution to the similarity control problem. Then, we present a method for synthesizing a maximally permissive similarity enforcing supervisor when the existence condition is satisfied.

In this paper, we study a supervisory control problem for plants and specifications modeled by nondeterministic automata. This problem requires to synthesize a nondeterministic supervisor such that the supervised plant is bisimilar to a given specification. We assume that a supervisor can observe not only the event occurrence but also the current state of the plant, and introduce a notion of completeness of a supervisor which guarantees that all nondeterministic transitions caused by events enabled by the supervisor are defined in the supervised plant. We define a notion of partial bisimulation between a given specification and the plant, and prove that it serves as a necessary and sufficient condition for the existence of a bisimilarity enforcing complete supervisor.